Papers by Wojciech Blajer
Journal of Theoretical and Applied Mechanics, 2006
Manipulating payloads with rotary cranes is challenging due to the underactuated nature of a syst... more Manipulating payloads with rotary cranes is challenging due to the underactuated nature of a system in which the number of control inputs/outputs is smaller than the number of degrees-of-freedom. In this paper, the outputs (specified in time load coordinates) lead to servoconstraints on the system. A specific methodology is then developed to solve the arising inverse dynamics problem. Governing equations are derived as a set of index three differential-algebraic equations in state variables and control inputs. An effective numerical code for solving the equations, based on the backward Euler method, is proposed. A feedforward control law obtained this way is then enhanced by a closed-loop control strategy with feedback of actual errors in the load position to provide stable tracking of the required reference load trajectory in presence of perturbations. Some results of numerical simulations are provided.
Journal of Theoretical and Applied Mechanics, 1983
Modelowanie Inżynierskie, 2006
Manipulating payloads with cranes can be challenging due to undesirable load pendulations induced... more Manipulating payloads with cranes can be challenging due to undesirable load pendulations induced by the crane motion and external perturbations. The problem gets increasingly difficult when the work environment is cluttered with obstacles. Automatic control schemes offer a high potential of rationalization. In this paper a methodology of constructing appropriate load trajectories allowing for one coordinated maneuver that omits the obstacles is addressed. The developed formulation leads then to the analysis of crane dynamics and synthesis of control in the specified motion. Some results of numerical simulations are reported.
Mechanical Sciences, Feb 19, 2013
Polish Journal of Sport and Tourism, Sep 1, 2013
Archive of Applied Mechanics, 1994
Synhesis of control of rotary crane executing a load prescribed motion part 1: theoretical background
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska, 2005
Independent Variable Formulations
CISM International Centre for Mechanical Sciences, 2009
ABSTRACT In Chapter 5 the dependent variable formulations for simulation of multibody systems wer... more ABSTRACT In Chapter 5 the dependent variable formulations for simulation of multibody systems were described. The derivation of equations of motion in terms of dependent states, though conceptually simple and easy to handle, leads to large-dimension governing DAEs, which results in computationally inefficient algorithms, burdened further with the constraint violation problem. An old and legitimate approach to the dynamics formulation is therefore to use a minimal number of independent state variables for a unique representation of motion by means of pure reduced-dimension ODEs. The numerical integration of the ODEs is usually by far more efficient compared to the integration of the governing DAEs, and the numerical solution is released from the problem of constraint violation. On the other hand, the minimal-form ODE formulations require often more modeling effort and skill. Effective and computer-oriented modeling procedures of this type are thus highly desirable.
Journal of Applied Mathematics and Mechanics, 1992
Sterowanie układów mechanicznych w ruchu programowym niezupełnym: teoria i przykłady zastosowań
Metoda więzów masowych w modelowaniu dynamiki układów wieloczłonowych
Modelowanie i symulacja układów wieloczłonowych
Efektywne wyznaczanie reakcji w węzłach kinematycznych mechanizmów
Journal of Theoretical and Applied Mechanics, 2014
Manipulators with both active and passive joints are examples of underactuated systems, featured ... more Manipulators with both active and passive joints are examples of underactuated systems, featured by less control inputs than degrees of freedom. Due to the underactuation, in the trajectory tracking (servo-constraint) problem, the feed-forward control obtained from an inverse model is influenced by internal dynamics of the system, leading to a more involved control design than in the fully actuated case. It is demonstrated that a convenient approach to the problem solution is to formulate the underactuated system dynamics in the input-output normal form, with the arising governing equations formulated either as ODEs (ordinary differential equations) or DAEs (differential-algebraic equations). The interrelationship between the inverse dynamics control and the associated internal dynamics is then studied and illustrated using a planar manipulator with two active and one passive joint. Some simulation results for the sample case study are reported.
Archive of Applied Mechanics, Feb 1, 2015
The paper deals with underactuated mechanical systems, featured by less control inputs m than deg... more The paper deals with underactuated mechanical systems, featured by less control inputs m than degrees of freedom f , m < f , subject to m servo-constraints (specified in time outputs) on the system. The arising servo-constraint problem (inverse dynamics analysis) is discussed with an emphasis on the way the servo-constraints are realized, varying from orthogonal to tangential, and a geometrical illustration of the different realization types is provided. Depending on the way the servo-constraints are realized, the governing equations are formulated either as ordinary differential equations (ODEs) or differential-algebraic equations (DAEs), and some computational issues for the ODEs and DAEs are discussed. The existence or non-existence of an explicit solution to the governing equations is further discussed, related to so-called differentially flat problems (without internal dynamics) and non-flat problems (with internal dynamics). It is shown that in case of non-flat problems with orthogonal realization of servo-constraints, stability of the internal dynamics must be assured. Simple case studies are reported to illustrate the proposed formulations and methodologies.
Proceedings in applied mathematics & mechanics, Dec 1, 2009
Underactuated mechanical systems are systems with fewer control inputs than the degrees of freedo... more Underactuated mechanical systems are systems with fewer control inputs than the degrees of freedom, n m < , the relevant technical examples being e.g. cranes, aircrafts and flexible manipulators. The determination of an input control strategy that forces an underactuated system to complete a set of m specified motion tasks (servo-constraints) is a demanding problem. The solution is conditioned to differential flatness of the problem, denoted that all 2n state variables and m control inputs can algebraically be expressed, at least theoretically, in terms of the desired m outputs and their time derivatives up to a certain order. A more practical formulation, motivated hereafter, is to pose the problem as a set of differential-algebraic equations, and then obtain the solution numerically. The theoretical considerations are illustrated by a simple two-degree-of-freedom underactuated system composed of two rotating discs connected by a flexible rod (torsional spring), in which the prespecified motion of the first disc is actuated by the torque applied to the second disc, 2 = n and 1 = m. The determined control strategy is then verified experimentally on a laboratory stand representing the two-disc system.
Biology of Sport, Apr 11, 2013
Wyznaczanie sił mięśniowych i obciążeń w stawach kończyn dolnych podczas trójskoku
Modelowanie Inżynierskie, 2012
Inverse Simulation Study of Trampoline-Performed Somersaults
Courses and lectures, 2000
ABSTRACT Front and back somersaults on the trampoline are modeled. The developed mathematical mod... more ABSTRACT Front and back somersaults on the trampoline are modeled. The developed mathematical models are used to solve the inverse dynamics problem, in which the applied moments of muscle forces at the joints that result in an actual (recorded) motion are determined. The nature of the stunts, the way the human body is maneuvered and controlled can be studied. The calculated torques are then used as control signals for the dynamic simulation. This provides a way to check the inverse dynamics procedures. The influencc of typical control errors on somersault performance can be studied as well. Some examples of numerical calculations are reported.
Badania własności sprężystych wyczynowej odskoczni gimnastycznej
Modelowanie Inżynierskie, 2012
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Papers by Wojciech Blajer